5 (x12 12 An individual has preferences represented by the utility function U(x,

Question

5 (x12 12 An individual has preferences represented by the utility function U(x,y) many of the following statements are TRUE concerning her marginal rate of substitution? . If the individual has 4 units ofx and 36 units of y, she would be willing to trade a How maximum of 1/3 units of y to get 1 additional unit ofx. If the individual has 8 units of r and 2 units of y, the MRS of x for y at that point would be 1/2. . If the individual has 16 units of x and 4 units of y, she would be willing to trade a maximu m of 2 units of x to get 1 additional unit of y a. b. 2 C. d. None of the statements are true

Explanation / Answer

MUx = dU/dx = x-0.5.(x0.5 + y0.5)

MUy = dU/dy = y-0.5.(x0.5 + y0.5)

MRSxy = MUx/MUy = y0.5/x0.5

Statement 1 - MRSxy = 6/2 = 3 , therefore, statement is false

Statement 2 - MRSxy = 20.5/80.5 = 1/2 , therefore, statement is true

Statement 3 - MRSyx = 160.5/40.5 = 2 , therefore, statement is true

Option b is correct

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